Uniform convergence of wavelet expansions of Gaussian random processes

TL;DR

This paper establishes new theoretical results on the uniform convergence in probability of wavelet expansions applied to stationary Gaussian random processes, broadening understanding of their convergence properties.

Contribution

It provides the most general conditions under which wavelet expansions of stationary Gaussian processes converge uniformly in probability.

Findings

Uniform convergence in probability is achieved under broad conditions.

The results extend previous convergence theorems for Gaussian processes.

Wavelet expansions can reliably approximate stationary Gaussian processes.

Abstract

New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.